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ECL Calculation

Expected Credit Loss engines for IFRS 9, US CECL, and Ind AS 109.

IFRS 9 ECL

from creditriskengine.ecl.ifrs9.ecl_calc import ecl_12_month, ecl_lifetime

# Stage 1: 12-month ECL
ecl_1 = ecl_12_month(pd_12m=0.02, lgd=0.40, ead=1_000_000, eir=0.05)

# Stage 2: Lifetime ECL
ecl_2 = ecl_lifetime(
    pd_term_structure=[0.02, 0.025, 0.03, 0.035, 0.04],
    lgd=0.40,
    ead=1_000_000,
    eir=0.05,
)

Multi-Scenario Weighting

from creditriskengine.ecl.ifrs9.scenarios import weighted_ecl, Scenario

scenarios = [
    Scenario("base", 0.50, ecl_base),
    Scenario("downside", 0.30, ecl_down),
    Scenario("severe", 0.20, ecl_severe),
]
final_ecl = weighted_ecl(scenarios)

creditriskengine.ecl.ifrs9.ecl_calc

IFRS 9 ECL computation — 12-month and lifetime.

12-month ECL (Stage 1): ECL_12m = PD_12m * LGD * EAD * DF

Lifetime ECL (Stage 2 and 3): ECL_lifetime = Sum(t=1..T) [Marginal_PD(t) * LGD(t) * EAD(t) * DF(t)]

Reference: IFRS 9.5.5.1-5.5.20, IFRS 9.B5.5.28-B5.5.29.

discount_factors(eir, periods)

Calculate discount factors at the effective interest rate.

DF(t) = 1 / (1 + EIR)^t

Parameters:

Name Type Description Default
eir float

Effective interest rate (annualized).

 required
periods int

Number of periods.

 required

Returns:

Type Description
ndarray

Array of discount factors for periods 1..T.
Source code in creditriskengine\ecl\ifrs9\ecl_calc.py 
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def discount_factors(
    eir: float,
    periods: int,
) -> np.ndarray:
    """Calculate discount factors at the effective interest rate.

    DF(t) = 1 / (1 + EIR)^t

    Args:
        eir: Effective interest rate (annualized).
        periods: Number of periods.

    Returns:
        Array of discount factors for periods 1..T.
    """
    if eir <= -1.0:
        raise ValueError(f"EIR must be greater than -1, got {eir}")
    t = np.arange(1, periods + 1, dtype=np.float64)
    return 1.0 / (1.0 + eir) ** t

ecl_12_month(pd_12m, lgd, ead, eir=0.0)

Calculate 12-month ECL for Stage 1 exposures.

Formula

ECL_12m = PD_12m * LGD * EAD * DF(1)

Parameters:

Name Type Description Default
pd_12m float

12-month probability of default.

 required
lgd float

Loss given default.

 required
ead float

Exposure at default.

 required
eir float

Effective interest rate for discounting.

 0.0

Returns:

Type Description
float

12-month ECL amount.
Source code in creditriskengine\ecl\ifrs9\ecl_calc.py 
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def ecl_12_month(
    pd_12m: float,
    lgd: float,
    ead: float,
    eir: float = 0.0,
) -> float:
    """Calculate 12-month ECL for Stage 1 exposures.

    Formula:
        ECL_12m = PD_12m * LGD * EAD * DF(1)

    Args:
        pd_12m: 12-month probability of default.
        lgd: Loss given default.
        ead: Exposure at default.
        eir: Effective interest rate for discounting.

    Returns:
        12-month ECL amount.
    """
    df = 1.0 / (1.0 + eir) if eir > 0 else 1.0
    ecl = pd_12m * lgd * ead * df
    logger.debug(
        "12m ECL: PD=%.4f LGD=%.2f EAD=%.2f DF=%.4f ECL=%.2f",
        pd_12m, lgd, ead, df, ecl,
    )
    return ecl

ecl_lifetime(marginal_pds, lgds, eads, eir=0.0)

Calculate lifetime ECL for Stage 2/3 exposures.

Formula

ECL = Sum(t=1..T) [Marginal_PD(t) * LGD(t) * EAD(t) * DF(t)]

Parameters:

Name Type Description Default
marginal_pds ndarray

Array of marginal PDs for each period.

 required
lgds ndarray | float

LGD values (scalar or array per period).

 required
eads ndarray | float

EAD values (scalar or array per period).

 required
eir float

Effective interest rate for discounting.

 0.0

Returns:

Type Description
float

Lifetime ECL amount.
Source code in creditriskengine\ecl\ifrs9\ecl_calc.py 
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def ecl_lifetime(
    marginal_pds: np.ndarray,
    lgds: np.ndarray | float,
    eads: np.ndarray | float,
    eir: float = 0.0,
) -> float:
    """Calculate lifetime ECL for Stage 2/3 exposures.

    Formula:
        ECL = Sum(t=1..T) [Marginal_PD(t) * LGD(t) * EAD(t) * DF(t)]

    Args:
        marginal_pds: Array of marginal PDs for each period.
        lgds: LGD values (scalar or array per period).
        eads: EAD values (scalar or array per period).
        eir: Effective interest rate for discounting.

    Returns:
        Lifetime ECL amount.
    """
    periods = len(marginal_pds)
    dfs = discount_factors(eir, periods)

    if isinstance(lgds, (int, float)):
        lgds = np.full(periods, lgds)
    if isinstance(eads, (int, float)):
        eads = np.full(periods, eads)

    ecl = float(np.sum(marginal_pds * lgds * eads * dfs))
    logger.debug("Lifetime ECL: periods=%d ECL=%.2f", periods, ecl)
    return ecl

calculate_ecl(stage, pd_12m, lgd, ead, eir=0.0, marginal_pds=None, lgd_curve=None, ead_curve=None)

Unified ECL calculation dispatcher based on IFRS 9 stage.

Stage 1: 12-month ECL Stage 2/3/POCI: Lifetime ECL

Parameters:

Name Type Description Default
stage IFRS9Stage

IFRS 9 impairment stage.

 required
pd_12m float

12-month PD.

 required
lgd float

Loss given default (scalar).

 required
ead float

Exposure at default (scalar).

 required
eir float

Effective interest rate.

 0.0
marginal_pds ndarray | None

Marginal PD curve (required for lifetime ECL).

 None
lgd_curve ndarray | None

Optional LGD term structure.

 None
ead_curve ndarray | None

Optional EAD term structure.

 None

Returns:

Type Description
float

ECL amount.
Source code in creditriskengine\ecl\ifrs9\ecl_calc.py 
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def calculate_ecl(
    stage: IFRS9Stage,
    pd_12m: float,
    lgd: float,
    ead: float,
    eir: float = 0.0,
    marginal_pds: np.ndarray | None = None,
    lgd_curve: np.ndarray | None = None,
    ead_curve: np.ndarray | None = None,
) -> float:
    """Unified ECL calculation dispatcher based on IFRS 9 stage.

    Stage 1: 12-month ECL
    Stage 2/3/POCI: Lifetime ECL

    Args:
        stage: IFRS 9 impairment stage.
        pd_12m: 12-month PD.
        lgd: Loss given default (scalar).
        ead: Exposure at default (scalar).
        eir: Effective interest rate.
        marginal_pds: Marginal PD curve (required for lifetime ECL).
        lgd_curve: Optional LGD term structure.
        ead_curve: Optional EAD term structure.

    Returns:
        ECL amount.
    """
    if stage == IFRS9Stage.STAGE_1:
        return ecl_12_month(pd_12m, lgd, ead, eir)

    # Stage 2, 3, POCI: lifetime ECL
    if marginal_pds is None:
        raise ValueError("marginal_pds required for lifetime ECL (Stage 2/3/POCI)")

    lgd_input = lgd_curve if lgd_curve is not None else lgd
    ead_input = ead_curve if ead_curve is not None else ead
    return ecl_lifetime(marginal_pds, lgd_input, ead_input, eir)